V. Batyrev

Publications72
h-index28
Citations4,913
Highly Influential Citations489
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Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
We consider families ${\cal F}(\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomials…
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Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties
We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV1,...,Vr in a toric…
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On the Hodge structure of projective hypersurfaces in toric varieties
This paper generalizes classical results of Griffiths, Dolgachev and Steenbrink on the cohomology of hypersurfaces in weighted projective spaces. Given a $d$-dimensional projective simplicial toric…
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New Trends in Algebraic Geometry: Birational Calabi–Yau n -folds have equal Betti numbers
Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties over local number…
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Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs
Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a natural Kawamata…
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Manin's conjecture for toric varieties
We prove an asymptotic formula conjectured by Manin for the number of $K$-rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth projective toric…
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ON THE CLASSIFICATION OF SMOOTH PROJECTIVE TORIC VARIETIES
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Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry
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Tamagawa numbers of polarized algebraic varieties
Let ${\cal L} = (L, \| \cdot \|_v)$ be an ample metrized invertible sheaf on a smooth quasi-projective algebraic variety $V$ defined over a number field. Denote by $N(V,{\cal L},B)$ the number of…
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Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori
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